재무연구 제 권 호 (2009년 5월)
Asian Review of Financial Research, Vol., No..
pp.309~354
pp.309~354
Effective Portfolio Optimization Based on Random Matrix Theory
Cheoljun Eom Division of Business Administration, Pusan National University, Busan 609-735, Republic of Korea
Woo-Sung Jung Department of Physics and Basic Science Research Institute, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea, Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA
Taisei Kaizoji Division of Social Sciences, International Christian University, Tokyo 181-8585, Japan
Yong H. Kim College of Business, University of Cincinnati, OH 45221, USA
Jongwon Park Division of Business Administration, University of Seoul, Seoul 130-743, Republic of Korea
In this study, we investigate empirically whether the control of the correlation matrix via the random matrix theory (RMT) method can create a more efficient portfolio than the traditional Markowitz's model. The reasons for this improvement are also investigated. From the viewpoints of both the degree of efficiency and diversification, we find that the portfolio from the correlation matrix without the properties of the largest eigenvalue via the RMT method is more efficient than the one created from the conventional Markowitz’s model. Furthermore, we empirically confirm that the properties of the largest eigenvalue cause an increase in the value of the correlation matrix and a decrease in the degree of diversification, thus ultimately increasing the degree of portfolio risk. These results suggest that the properties of a market factor are negatively related to the degree of efficiency obtainable through the Markowitz's portfolio model. In addition, on the basis of the ex-ante test (using the expected stock returns and risk of the past period as well as actual data in the future period) we find that the performance of the observed RMT-based efficient portfolio is superior to that of the portfolio from Markowitz's model. These results demonstrate that the improvement of Markowitz's portfolio model via the control of the correlation matrix can be a source of significant practical utility.
Cheoljun Eom
Woo-Sung Jung
Taisei Kaizoji
Yong H. Kim
Jongwon Park
In this study, we investigate empirically whether the control of the correlation matrix via the random matrix theory (RMT) method can create a more efficient portfolio than the traditional Markowitz's model. The reasons for this improvement are also investigated. From the viewpoints of both the degree of efficiency and diversification, we find that the portfolio from the correlation matrix without the properties of the largest eigenvalue via the RMT method is more efficient than the one created from the conventional Markowitz’s model. Furthermore, we empirically confirm that the properties of the largest eigenvalue cause an increase in the value of the correlation matrix and a decrease in the degree of diversification, thus ultimately increasing the degree of portfolio risk. These results suggest that the properties of a market factor are negatively related to the degree of efficiency obtainable through the Markowitz's portfolio model. In addition, on the basis of the ex-ante test (using the expected stock returns and risk of the past period as well as actual data in the future period) we find that the performance of the observed RMT-based efficient portfolio is superior to that of the portfolio from Markowitz's model. These results demonstrate that the improvement of Markowitz's portfolio model via the control of the correlation matrix can be a source of significant practical utility.
